Wednesday, 21 September 2016
The Skyscraper Challenge for all Ages!
Hi everyone!
Thanks for tuning into my first blog post. This week, in my Mathematics Teaching course for Intermediate/Senior, my professor sectioned us off into groups to complete the Skyscraper Challenge. For those of you who have never heard of this activity, I have provided a picture, as well as a video below to help you visualize.
In this activity, we used linking cubes to make towers. Since this is a 4x4 square we were only able to use linking cube towers in groups of 1, 2, 3, or 4. For all of you Sudoku lovers out there, this game is very similar because each row and column must have one set of 1, 2, 3, and 4 linking cube towers; repeats are not allowed. The numbers along the sides of the square represent how many "towers of linking cubes" you will be able to see when you look from that direction.
Before my class began the activity, we were given a limited amount of instruction, and we were not explicitly told what the numbers on the sides of the square represented. My group struggled for about 10-15 minutes on our own; we asked each other questions, tested out conjectures, and failed. We were stumped. Finally, we asked our teacher for a bit more guidance, and also looked to the internet as a resource, in order to help us find a clue to solve the puzzle. Once we discovered that we needed to be able to see a given number of "towers/buildings" from each square, we set off to solve the problem! It was fun and exciting to play around with the towers of linking cubes, in order to see what satisfied all of the requirements of the given puzzle. I felt myself smiling and laughing with my group, and I almost didn't want to stop when our teacher finally called our class in for a group discussion of the activity.
My teacher informed us that this activity was actually used in a grade 1 classroom to help them develop spacial reasoning. Some of you may be wondering how a grade 1 student, who is barely 6 years old, can solve a puzzle that is still challenging for university students. At first, I was questioning this too, but then I realized that sometimes, without meaning to, we can underestimate the capabilities of our students.
I remember when I was little, and being told that I was too young to do or learn something. My parents would tell me that I could do/learn this when I was older. I would badger them with questions like, "Why do I have to be older? How much older do I have to be? When exactly will you be able to tell me these things?" and as a last resort, when they still wouldn't give into me, I would use the, "I'm old enough now! I can understand things!" card. I was always frustrated when my age hindered me from learning news things, and I could not wait to be older!
I wonder if teaching is similar. My professor gave this activity to a grade 1 class, not knowing if they would be able to solve it or not. However, the results surprised her. She found that these students discovered solutions to the puzzle through play based learning. These students did not get frustrated by not knowing the answer, they just continued to try, play and learn. One of my peers from my English Teaching class brought up the point that we wait until students reach a certain age to teach them about new topics. In math, we deem that by grade 11, students will be capable of learning functions. What makes a grade 10 student different from a grade 11 student? One year? We believe that when students are 15, they are not ready to learn about functions, but when they turn 16, they have reached the perfect age. Is this right? Could it be that by waiting to teach students about these complex concepts, that we are reinforcing the giant learning gap that exists between each grade? What would happen if we introduced topics earlier? Would this help ease students anxiety over mathematics if they were exposed to these concepts at an earlier age, so that by the time that they reached the required age of learning, these concepts would already be familiar?
I know that I have raised a lot of questions that I don't necessarily have the answers to. However, I feel that this issue is something to consider. Sometimes, we do make assumptions about students based on their age, grade level, or stream (academic, applied or locally developed). By giving students the opportunity to try activities that we feel may be above their grade level, we may be surprised by what we see. If we find that students are struggling to understand the concept, we can provide more scaffolding and guidance to help them along; however, if we notice that they are able to solve these problems on their own with very little assistance, our assumptions will no longer be valid. We need to give students a chance to try new things, in order to expose them to these concepts/strategies/ways of thinking earlier, so that their learning will be continuous and familiar, instead of abrupt, disconnected, and something to be feared.
If you would like to use the Skyscraper activity in your classroom, or would simply like to solve the puzzle yourself, there are daily puzzles available at the following link: https://www.brainbashers.com/skyscrapers.asp
Thank you all for reading, and have a wonderful day!
Dayna
Thanks for tuning into my first blog post. This week, in my Mathematics Teaching course for Intermediate/Senior, my professor sectioned us off into groups to complete the Skyscraper Challenge. For those of you who have never heard of this activity, I have provided a picture, as well as a video below to help you visualize.
Before my class began the activity, we were given a limited amount of instruction, and we were not explicitly told what the numbers on the sides of the square represented. My group struggled for about 10-15 minutes on our own; we asked each other questions, tested out conjectures, and failed. We were stumped. Finally, we asked our teacher for a bit more guidance, and also looked to the internet as a resource, in order to help us find a clue to solve the puzzle. Once we discovered that we needed to be able to see a given number of "towers/buildings" from each square, we set off to solve the problem! It was fun and exciting to play around with the towers of linking cubes, in order to see what satisfied all of the requirements of the given puzzle. I felt myself smiling and laughing with my group, and I almost didn't want to stop when our teacher finally called our class in for a group discussion of the activity.
My teacher informed us that this activity was actually used in a grade 1 classroom to help them develop spacial reasoning. Some of you may be wondering how a grade 1 student, who is barely 6 years old, can solve a puzzle that is still challenging for university students. At first, I was questioning this too, but then I realized that sometimes, without meaning to, we can underestimate the capabilities of our students.
I remember when I was little, and being told that I was too young to do or learn something. My parents would tell me that I could do/learn this when I was older. I would badger them with questions like, "Why do I have to be older? How much older do I have to be? When exactly will you be able to tell me these things?" and as a last resort, when they still wouldn't give into me, I would use the, "I'm old enough now! I can understand things!" card. I was always frustrated when my age hindered me from learning news things, and I could not wait to be older!
I wonder if teaching is similar. My professor gave this activity to a grade 1 class, not knowing if they would be able to solve it or not. However, the results surprised her. She found that these students discovered solutions to the puzzle through play based learning. These students did not get frustrated by not knowing the answer, they just continued to try, play and learn. One of my peers from my English Teaching class brought up the point that we wait until students reach a certain age to teach them about new topics. In math, we deem that by grade 11, students will be capable of learning functions. What makes a grade 10 student different from a grade 11 student? One year? We believe that when students are 15, they are not ready to learn about functions, but when they turn 16, they have reached the perfect age. Is this right? Could it be that by waiting to teach students about these complex concepts, that we are reinforcing the giant learning gap that exists between each grade? What would happen if we introduced topics earlier? Would this help ease students anxiety over mathematics if they were exposed to these concepts at an earlier age, so that by the time that they reached the required age of learning, these concepts would already be familiar?
I know that I have raised a lot of questions that I don't necessarily have the answers to. However, I feel that this issue is something to consider. Sometimes, we do make assumptions about students based on their age, grade level, or stream (academic, applied or locally developed). By giving students the opportunity to try activities that we feel may be above their grade level, we may be surprised by what we see. If we find that students are struggling to understand the concept, we can provide more scaffolding and guidance to help them along; however, if we notice that they are able to solve these problems on their own with very little assistance, our assumptions will no longer be valid. We need to give students a chance to try new things, in order to expose them to these concepts/strategies/ways of thinking earlier, so that their learning will be continuous and familiar, instead of abrupt, disconnected, and something to be feared.
If you would like to use the Skyscraper activity in your classroom, or would simply like to solve the puzzle yourself, there are daily puzzles available at the following link: https://www.brainbashers.com/skyscrapers.asp
Thank you all for reading, and have a wonderful day!
Dayna
Monday, 19 September 2016
Meet the Blogger
Hi everyone!
In case you are a little curious about the person behind the blog posts, I thought I would introduce myself!
My name is Dayna Perry and I am a math-fanatic. What can I say? I love the challenge of solving a math problem, and I live for the rush of excitement that comes from finding a solution (one of many, in some cases)! I am also a sucker for numbers, but even numbers are my favourite! I love Sudoku, nano-grams, and Reno-grams; basically any game that allows me to work and play with numbers has me fascinated! I will also apologize in advance for my overzealous use of exclamation marks in my writing. For some reason, exclamation marks tend to make everything seem more exciting, especially when placed at the end of a sentence relating to the topic of math. Math tends to be seen as a boring subject, so it couldn't hurt to throw a few exclamation marks in to help spice up this seemingly dull (never!) topic. Could it?
All joking matters aside, math is a wonderful subject. I have always enjoyed math, and have loved teaching others when they have struggled to understand some of the basic or more complex concepts. For this reason, I chose to pursue a career in math education. I am heading into my fifth and final year, which is also known as the year of teacher's college. This blog will be used as a tool to help me reflect on my math teaching experience. I hope to use this year to learn how to make math meaningful and relevant for my students, so that they will not have to ask me, "Ms. Perry, what is the point? Why am I learning this? When am I ever going to use this in the real world?". My mission throughout the year, and throughout my teaching career is to help students answer these questions on their own, by providing them with real world examples and applications. I want my students to have fun! Why is it acceptable for the math classroom to be boring? Math should never be boring...if it is, then we have a serious problem on our hands. I want to be able to restore some of the confidence that has been lost along the way for many of my students who believe in the stereotypical "math person/type". I need to help my students realize that we are all capable of learning math, and the true beauty of math is that it is universal; everyone can learn to understand it and find meaning in it.
Throughout this year of teacher's college I hope to make mistakes and learn from them. I hope that you will join me in my adventure, and hopefully we will be able to make mistakes together, and learn from one another!
To end this post on a good note, here is a math joke for you to enjoy!
+Dayna+
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